In this research, we focus on a common fixed point problem of a nonexpansive semigroup with the generalized viscosity methods for implicit iterative algorithms. Our main objective is to construct the new strong convergence theorems under certain appropriate conditions in uniformly convex and uniformly smooth Banach spaces. Specifically, the main results make a contribution to the implicit midpoint theorems. The findings for theorems in Hilbert spaces and the other forms of a nonexpansive semigroup can be used in several practical purposes. Finally, a numerical example in 3 dimensions is provided to support our main results.
{"title":"The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces","authors":"C. Jaiboon, S. Plubtieng, Phayap Katchang","doi":"10.22436/JNSA.011.06.02","DOIUrl":"https://doi.org/10.22436/JNSA.011.06.02","url":null,"abstract":"In this research, we focus on a common fixed point problem of a nonexpansive semigroup with the generalized viscosity methods for implicit iterative algorithms. Our main objective is to construct the new strong convergence theorems under certain appropriate conditions in uniformly convex and uniformly smooth Banach spaces. Specifically, the main results make a contribution to the implicit midpoint theorems. The findings for theorems in Hilbert spaces and the other forms of a nonexpansive semigroup can be used in several practical purposes. Finally, a numerical example in 3 dimensions is provided to support our main results.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"17 1","pages":"746-761"},"PeriodicalIF":0.0,"publicationDate":"2018-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85394011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a system of multicolored disordered lattice gas in a volume Λ of Zd driven by a disordered Markov generator similar to that of Faggionato and Martinelli [A. Faggionato, F. Martinelli, Probab. Theory Related Fields, 127 (2003), 535–608]. The aim of our work is to give a new and elementary computation of the spectral gap of multicolored disordered lattice gas which is an important step towards obtaining the hydrodynamic limit.
{"title":"On spectral gap for multicolored disordered lattice gas of exclusion processes","authors":"A. Touati, Laila Benaon, Halim zeghdoudi","doi":"10.22436/JNSA.011.05.12","DOIUrl":"https://doi.org/10.22436/JNSA.011.05.12","url":null,"abstract":"We consider a system of multicolored disordered lattice gas in a volume Λ of Zd driven by a disordered Markov generator similar to that of Faggionato and Martinelli [A. Faggionato, F. Martinelli, Probab. Theory Related Fields, 127 (2003), 535–608]. The aim of our work is to give a new and elementary computation of the spectral gap of multicolored disordered lattice gas which is an important step towards obtaining the hydrodynamic limit.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"17 1","pages":"723-733"},"PeriodicalIF":0.0,"publicationDate":"2018-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74819784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is concerned with the existence of multiple positive almost periodic solutions for a nonlinear integral equation. By using Avery-Henderson and Leggett-Williams multiple fixed point theorems on cones, the existence theorems of multiple positive almost periodic solutions for the addressed integral equation are established under some sufficient assumptions. An example is given to illustrate our results.
{"title":"Multiple positive almost periodic solutions for some nonlinear integral equations","authors":"H. Ding, J. Nieto, Q. Zou","doi":"10.22436/JNSA.011.05.11","DOIUrl":"https://doi.org/10.22436/JNSA.011.05.11","url":null,"abstract":"This paper is concerned with the existence of multiple positive almost periodic solutions for a nonlinear integral equation. By using Avery-Henderson and Leggett-Williams multiple fixed point theorems on cones, the existence theorems of multiple positive almost periodic solutions for the addressed integral equation are established under some sufficient assumptions. An example is given to illustrate our results.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"25 1","pages":"713-722"},"PeriodicalIF":0.0,"publicationDate":"2018-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72660445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the concept of the strong-positive cone in a lattice-ordered group (G,6, ·) and define the continuous latticeordered group. We also investigate the C-topology and bi-C-topology given on a lattice-ordered group. The main results obtained in this paper are as follows: (1) (G,6, ·) is a continuous lattice-ordered group if and only if (G,6) is a continuous poset; (2) for the bi-C-topology τ in a continuous lattice-ordered group (G,6, ·), (G, ·, τ) is a topological group and (G,6, τ) is a topological lattice.
{"title":"A topology on lattice-ordered groups","authors":"H. Wu, Qingguo Li, Bin Yu","doi":"10.22436/JNSA.011.05.10","DOIUrl":"https://doi.org/10.22436/JNSA.011.05.10","url":null,"abstract":"We introduce the concept of the strong-positive cone in a lattice-ordered group (G,6, ·) and define the continuous latticeordered group. We also investigate the C-topology and bi-C-topology given on a lattice-ordered group. The main results obtained in this paper are as follows: (1) (G,6, ·) is a continuous lattice-ordered group if and only if (G,6) is a continuous poset; (2) for the bi-C-topology τ in a continuous lattice-ordered group (G,6, ·), (G, ·, τ) is a topological group and (G,6, τ) is a topological lattice.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"9 1","pages":"701-712"},"PeriodicalIF":0.0,"publicationDate":"2018-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77153406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the split monotone variational inclusion problem in Hilbert spaces. By assuming the existence of solutions, we introduce an iterative algorithm, in which the stepsizes does not need any prior information about the operator norm, and show its convergence theorem. Some applications and numerical experiments of the considered problem are also discussed.
{"title":"Finding a solution of split null point of the sum of monotone operators without prior knowledge of operator norms in Hilbert spaces","authors":"Montira Suwannaprapa, N. Petrot","doi":"10.22436/jnsa.011.05.09","DOIUrl":"https://doi.org/10.22436/jnsa.011.05.09","url":null,"abstract":"In this paper, we consider the split monotone variational inclusion problem in Hilbert spaces. By assuming the existence of solutions, we introduce an iterative algorithm, in which the stepsizes does not need any prior information about the operator norm, and show its convergence theorem. Some applications and numerical experiments of the considered problem are also discussed.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"11 1","pages":"683-700"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88740348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article mainly studies the order-reduction of the classical Crank-Nicolson finite difference (CNFD) scheme for the Riesz space fractional order differential equations (FODEs) with a nonlinear source function and delay on a bounded domain. For this reason, the classical CNFD scheme for the Riesz space FODE and the existence, stability, and convergence of the classical CNFD solutions are first recalled. And then, a reduced-order extrapolating CNFD (ROECNFD) scheme containing very few degrees of freedom but holding the fully second-order accuracy for the Riesz space FODEs is established by means of proper orthogonal decomposition and the existence, stability, and convergence of the ROECNFD solutions are discussed. Finally, some numerical experiments are presented to illustrate that the ROECNFD scheme is far superior to the classical CNFD one and to verify the correctness of theoretical results. This indicates that the ROECNFD scheme is very effective for solving the Riesz space FODEs with a nonlinear source function and delay.
{"title":"A reduced-order extrapolating Crank-Nicolson finite difference scheme for the Riesz space fractional order equations with a nonlinear source function and delay","authors":"Yanhua Cao, Zhendong Luo","doi":"10.22436/JNSA.011.05.08","DOIUrl":"https://doi.org/10.22436/JNSA.011.05.08","url":null,"abstract":"This article mainly studies the order-reduction of the classical Crank-Nicolson finite difference (CNFD) scheme for the Riesz space fractional order differential equations (FODEs) with a nonlinear source function and delay on a bounded domain. For this reason, the classical CNFD scheme for the Riesz space FODE and the existence, stability, and convergence of the classical CNFD solutions are first recalled. And then, a reduced-order extrapolating CNFD (ROECNFD) scheme containing very few degrees of freedom but holding the fully second-order accuracy for the Riesz space FODEs is established by means of proper orthogonal decomposition and the existence, stability, and convergence of the ROECNFD solutions are discussed. Finally, some numerical experiments are presented to illustrate that the ROECNFD scheme is far superior to the classical CNFD one and to verify the correctness of theoretical results. This indicates that the ROECNFD scheme is very effective for solving the Riesz space FODEs with a nonlinear source function and delay.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"47 1","pages":"672-682"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80360286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We say that a function f : [a,b]→ R is (φ, δ)-Lipschitzian, where δ > 0 and φ : [0,∞)→ [0,∞), if |f(x) − f(y)| 6 φ(|x− y|) + δ, (x,y) ∈ [a,b]× [a,b]. In this work, some Hadamard’s type inequalities are established for the class of (φ, δ)-Lipschitzian mappings. Moreover, some applications to convex functions with a continuous Caputo fractional derivative are also discussed.
{"title":"New integral inequalities and their applications to convex functions with a continuous Caputo fractional derivative","authors":"B. Ahmad, M. Jleli, B. Samet","doi":"10.22436/jnsa.011.05.07","DOIUrl":"https://doi.org/10.22436/jnsa.011.05.07","url":null,"abstract":"We say that a function f : [a,b]→ R is (φ, δ)-Lipschitzian, where δ > 0 and φ : [0,∞)→ [0,∞), if |f(x) − f(y)| 6 φ(|x− y|) + δ, (x,y) ∈ [a,b]× [a,b]. In this work, some Hadamard’s type inequalities are established for the class of (φ, δ)-Lipschitzian mappings. Moreover, some applications to convex functions with a continuous Caputo fractional derivative are also discussed.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"13 1 1","pages":"658-671"},"PeriodicalIF":0.0,"publicationDate":"2018-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81551875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a general system of variational inclusions in Banach Spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a λ-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theorems in uniformly convex and 2-uniformly smooth Banach spaces. The results presented in the paper improve and extend various results in the existing literatures. Moreover, some applications to monotone variational inequality problem and convex minimization problem are presented.
{"title":"Approximation of solutions to a general system of variational inclusions in Banach spaces and applications","authors":"Hongbo Liu","doi":"10.22436/jnsa.011.05.06","DOIUrl":"https://doi.org/10.22436/jnsa.011.05.06","url":null,"abstract":"In this paper, a general system of variational inclusions in Banach Spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a λ-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theorems in uniformly convex and 2-uniformly smooth Banach spaces. The results presented in the paper improve and extend various results in the existing literatures. Moreover, some applications to monotone variational inequality problem and convex minimization problem are presented.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"8 1","pages":"644-657"},"PeriodicalIF":0.0,"publicationDate":"2018-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88287453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Some problems from modern physics and science can be described in terms of partial differential equations with nonlocal conditions. In this paper, a numerical method which employs the orthonormal Bernstein polynomials basis is implemented to give the approximate solution of integro-differential parabolic equation with purely nonlocal integral conditions. The properties of orthonormal Bernstein polynomials, and the operational matrices for integration, differentiation and the product are introduced and are utilized to reduce the solution of the given integro-differential parabolic equation to the solution of algebraic equations. An illustrative example is given to demonstrate the validity and applicability of the new technique.
{"title":"Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials","authors":"Abdelkrim Bencheikh, L. Chiter, Tongxing Li","doi":"10.22436/JNSA.011.05.04","DOIUrl":"https://doi.org/10.22436/JNSA.011.05.04","url":null,"abstract":"Some problems from modern physics and science can be described in terms of partial differential equations with nonlocal conditions. In this paper, a numerical method which employs the orthonormal Bernstein polynomials basis is implemented to give the approximate solution of integro-differential parabolic equation with purely nonlocal integral conditions. The properties of orthonormal Bernstein polynomials, and the operational matrices for integration, differentiation and the product are introduced and are utilized to reduce the solution of the given integro-differential parabolic equation to the solution of algebraic equations. An illustrative example is given to demonstrate the validity and applicability of the new technique.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"37 1","pages":"624-634"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81339216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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